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2 Netka M.

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Differential difference inequalities related to parabolic functional differential equations

Netka M.

Opuscula Mathematica

2010

Vol. 30, no. 1

95-115

Initial boundary value problems for nonlinear parabolic functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A comparison theorem for differential difference inequalities is proved. Sufficient conditions for the convergence of the method of lines is given. Nonlinear estimates of the Perron type for given operators with respect to functional variables are used. Results obtained in the paper can be applied to differential integral problems and to equations with deviated variables.

Uniqueness of solutions of a generalized Cauchy problem for a system of first order partial functional differential equations

Netka M.

Opuscula Mathematica

2009

Vol. 29, no. 1

69-79

The paper is concerned with weak solutions of a generalized Cauchy problem for a nonlinear system of first order differential functional equations. A theorem on the uniqueness of a solution is proved. Nonlinear estimates of the Perron type are assumed. A method of integral functional inequalities is used.